Conditioned Higher Moment Portfolio Optimisation Using Optimal Control

Within a traditional context of myopic discrete-time mean-variance portfolio investments, the problem of conditioned optimisation, in which predictive information about returns contained in a signal is used to inform the choice of portfolio weights, was first expressed and solved in concrete terms by [1]. An optimal control formulation of conditioned portfolio problems was proposed and justified by [2]. This opens up the possibility of solving variants of the basic problem that do not allow for closed-form solutions through the use of standard numerical algorithms used for the discretisation of optimal control problems. The present paper applies this formulation to set and solve variants of the conditioned portfolio problem which use the third and fourth moments as well as the variance. Using backtests over a realistic data set, the performance of strategies resulting from conditioned optimisation is then compared to that obtained using analogous optimisation strategies which do not exploit conditioning information. In particular, we report on both ex ante improvements to the accessible expected return-risk boundaries and the ex post results obtained.